Hi,
Then the problem must come from the settings you have under the "Emails" section of the HikaShop configuration.
HikaShop sends the emails by default in HTML, but the test email of Joomla is a simple text email and there is a lot less issues with them. So you could try deactivate the HTML settings there and see if that helps.
Also, sometimes the bounce email address configured there is wrong. Try leaving it empty, or better, ask your hosting company what it should be.
Some other email servers are quite picky with the charset encoding of the emails and thus you might need to change that setting too.
The best is to check with the hosting.
First, check the menu Customers>Emails history. There, you'll see the emails that HikaShop sent to your email server.
If you see the email there but not in your inbox, then the problem is not a HikaShop problem. It's either the email settings or the email server, or it went in the spam folder.